Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
how would you do 93?
![### Solving for Angles in Quadrilaterals
This section covers how to solve for specific angles in quadrilateral figures using given information and algebraic equations.
#### Example 1
Consider the quadrilateral \(S, T, \text{(unnamed)}, \text{(unnamed)}\):
- Angle at the unnamed point on the top right: \(75^\circ\)
- Vertical angle on the left: \(22x + 2\)
- Vertical angle on the right: \(30x - 7\)
There is a handwritten note indicating summing two of these angles (\(75\) and an unknown angle on the right) equals \(105\).
#### Example 2
Given another quadrilateral \(WXYZ\):
- Angle \(WY = 58^\circ\)
- Top right angle \(measure = 5x - 5\)
- Bottom edge measure for line segment \(ZY = 4x + 19\)
#### Step-by-Step Solution for Example 2
To find the measure of angle \( \angle X \):
1. Apply the rules of quadrilaterals: The sum of interior angles in any quadrilateral is always \(360^\circ\).
2. Set up the equation using the known angles and expressions:
\[
\angle W + \angle X + \angle Y + \angle Z = 360^\circ
\]
Here, \( \angle Y = 58^\circ \).
3. Use algebra to solve for \(x\) and then determine \( \angle X \) using the expression \( 5x - 5 \).
### Diagrams
**Diagram 1** depicts a quadrilateral:
- Each corner is labeled.
- Specific angles and algebraic expressions are provided near each vertex.
- A note calculates \(75 + ? = 105\).
**Diagram 2** includes:
- Named quadrilateral, \(WXYZ\).
- Specific measures and algebraic expressions for angles and sides.
### Conclusion
Through understanding and applying properties and theorems related to quadrilaterals, one can determine unknown angles and sides. This involves setting up and solving equations based on given measures and relationships within the figure.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c3597d8-30c2-4840-bf6e-c951942ae65e%2F25474d74-4ab2-4625-b4c0-24fbcfce00e0%2Fc0xhjhi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving for Angles in Quadrilaterals
This section covers how to solve for specific angles in quadrilateral figures using given information and algebraic equations.
#### Example 1
Consider the quadrilateral \(S, T, \text{(unnamed)}, \text{(unnamed)}\):
- Angle at the unnamed point on the top right: \(75^\circ\)
- Vertical angle on the left: \(22x + 2\)
- Vertical angle on the right: \(30x - 7\)
There is a handwritten note indicating summing two of these angles (\(75\) and an unknown angle on the right) equals \(105\).
#### Example 2
Given another quadrilateral \(WXYZ\):
- Angle \(WY = 58^\circ\)
- Top right angle \(measure = 5x - 5\)
- Bottom edge measure for line segment \(ZY = 4x + 19\)
#### Step-by-Step Solution for Example 2
To find the measure of angle \( \angle X \):
1. Apply the rules of quadrilaterals: The sum of interior angles in any quadrilateral is always \(360^\circ\).
2. Set up the equation using the known angles and expressions:
\[
\angle W + \angle X + \angle Y + \angle Z = 360^\circ
\]
Here, \( \angle Y = 58^\circ \).
3. Use algebra to solve for \(x\) and then determine \( \angle X \) using the expression \( 5x - 5 \).
### Diagrams
**Diagram 1** depicts a quadrilateral:
- Each corner is labeled.
- Specific angles and algebraic expressions are provided near each vertex.
- A note calculates \(75 + ? = 105\).
**Diagram 2** includes:
- Named quadrilateral, \(WXYZ\).
- Specific measures and algebraic expressions for angles and sides.
### Conclusion
Through understanding and applying properties and theorems related to quadrilaterals, one can determine unknown angles and sides. This involves setting up and solving equations based on given measures and relationships within the figure.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning